Without knowing which Toyota, I can't get too specific, but it sounds like a case of being unfamiliar with a rental car.
CarPlay likely came up as default because you had a route in progress. Somewhere either on the dash or the screen was a "home" button that would have taken you out of CarPlay and to the vehicle's default infotainment screen, where you could choose radio.
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Failing that, the eight white buttons (which is actually one big one) at the bottom of the sidebar take you to the main CarPlay menu:
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And in there is a "Toyota" app that also offers audio options.
There's also a "Home"button in the sidebar in that view (it may look different depending on the vehicle) that takes you back to a main screen.
One other note: the three apps in the sidebar are the most recently used. I know you've never used Apple Music---but it has to default somewhere, so it's designed to default to the three most common functions---phone, nav and music. If you were to use the Podcast or Audiobooks app, that would take the place of one of the other apps in the sidebar. Have Siri send or read a text message to you, and Messages would be in your last three on the sidebar, and so on.
Flaw in the logic: Very few people are keeping phones ten or more years. Most people get a new phone (especially people who have iPhones) every three to six years, and the software within---including CarPlay and the apps it makes available) are updated several times yearly while you own that phone. And there are firmware updates for it within the vehicle itself.
Compare that to whatever came with the vehicle when you bought it. You're light years ahead by having the phone and its updates.